scholarly journals Affineness and chromatic homotopy theory

2015 ◽  
Vol 8 (2) ◽  
pp. 476-528 ◽  
Author(s):  
Akhil Mathew ◽  
Lennart Meier
2020 ◽  
Vol 220 (3) ◽  
pp. 737-845
Author(s):  
Tobias Barthel ◽  
Tomer M. Schlank ◽  
Nathaniel Stapleton

AbstractInspired by the Ax–Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the approximation problem in chromatic homotopy theory. More precisely, we show that the ultraproduct of the E(n, p)-local categories over any non-principal ultrafilter on the set of prime numbers is equivalent to the ultraproduct of certain algebraic categories introduced by Franke. This shows that chromatic homotopy theory at a fixed height is asymptotically algebraic.


2018 ◽  
Vol 117 (6) ◽  
pp. 1135-1180 ◽  
Author(s):  
Tobias Barthel ◽  
Drew Heard

2021 ◽  

This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.


2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.


1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead

Sign in / Sign up

Export Citation Format

Share Document